A1 Journal article (refereed)
Geodesic ray transform with matrix weights for piecewise constant functions (2020)
Ilmavirta, J., & Railo, J. (2020). Geodesic ray transform with matrix weights for piecewise constant functions. Annales Academiae Scientiarum Fennicae-Mathematica, 45(2), 1095-1102. https://doi.org/10.5186/aasfm.2020.4558
JYU authors or editors
Publication details
All authors or editors: Ilmavirta, Joonas; Railo, Jesse
Journal or series: Annales Academiae Scientiarum Fennicae-Mathematica
ISSN: 1239-629X
eISSN: 1798-2383
Publication year: 2020
Volume: 45
Issue number: 2
Pages range: 1095-1102
Publisher: Suomalainen tiedeakatemia
Publication country: Finland
Publication language: English
DOI: https://doi.org/10.5186/aasfm.2020.4558
Publication open access: Openly available
Publication channel open access: Open Access channel
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/71316
Abstract
We show injectivity of the geodesic X-ray transform on piecewise constant functions when the transform is weighted by a continuous matrix weight. The manifold is assumed to be compact and nontrapping of any dimension, and in dimension three and higher we assume a foliation condition. We make no assumption regarding conjugate points or differentiability of the weight. This extends recent results for unweighted transforms.
Keywords: inverse problems
Free keywords: geodesic ray transform; matrix weight; integral geometry
Contributing organizations
Related projects
- Ray tomography for imaging the Earth
- Ilmavirta, Joonas
- Academy of Finland
- Centre of Excellence in Inverse Problems Research
- Salo, Mikko
- Academy of Finland
Ministry reporting: Yes
Reporting Year: 2020
JUFO rating: 2